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Practical crack control during the construction of precast segmental box girder bridges
Computers and Structures 83 (2005) 2584–2593 www.elsevier.com/locate/compstruc
Practical crack control during the construction of precast segmental box girder bridges Do-Young Moon a, Jongsung Sim a, Hongseob Oh a b
b,*
Department of Civil and Environmental Engineering, Hanyang University, 1271 Sa1-dong, Ansan 425-791, South Korea Department of Civil Engineering, Jinju National University, 150 Chilam-dong, Jinju, Kyeongnam 660-758, South Korea Received 7 October 2004; accepted 16 May 2005 Available online 12 September 2005
Abstract Cracks that occurred in the bottom slab of a precast segmental bridge were investigated through a construction sequence analysis, which revealed that the cracks were caused by excessive deformation during temporary post-tensioning while joining the segments. In addition, a parametric study was performed to evaluate the effects of the prestressing sequence, bottom slab thickness, and position of the prestressing anchors. The structural behavior of the girder sections was greatly affected by the thickness of the bottom slab and the position of prestressing anchors, but not by the prestressing sequence. Based on the results, a construction method that prevents the cracks is proposed. 2005 Elsevier Ltd. All rights reserved. Keywords: Construction sequence analysis; FE analysis; PC box girder; Precast segmental bridge; Structural behavior; Temporary prestressing
1. Introduction Prestressed concrete box girder bridges were developed in Europe in the 1950s, and are widely used in both mid- and long-span bridge construction for reasons of economy and aesthetics. In particular, quality control is easily ensured when precast segmental box girder bridges are constructed using the span-by-span method, because the mechanization of the construction work allows contracts for the spans to be awarded for a term that extends over many construction projects. Therefore, this technique has been used in many of the prestressed concrete girder bridges constructed in Korea since 1980. * Corresponding author. Tel.: +82 55 751 3299; fax: +82 55 751 3209. E-mail address: [email protected] (H. Oh).
The Seo-hae grand bridge, which is an oversea bridge with a total length of 7.3 km that was completed in early 2001, also used this method, except for the cable-stayed portion of the bridge, as shown in Fig. 1. In precast segmental construction, the bridge segments are constructed offsite. They are then trucked or barged to the bridge site and lifted into place with a crane or gantry, as depicted in Fig. 2. The size of the segments is affected primarily by the method of transport that is available. For example, a bridge located near a navigable waterway can use larger segments because they can be transported by barge. If the segments must be transported by truck, they are generally limited to widths that can travel within a roadway lane. In the span-by-span method, a segmental box is placed on the pier, moved by an overslung truss, and posttensioned after it has been erected.
0045-7949/$ - see front matter 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.compstruc.2005.05.001
D.-Y. Moon et al. / Computers and Structures 83 (2005) 2584–2593
2585
PSM FCM
Dangjin
PSM Cable stayed Bridge
P100 A2 P74
PSM P56 P55 FCM
Pier87~ Pier88
P41 P40
Pyungtak
Pier5~ Pier6
Fig. 1. The bridge plans and inspected bridge section.
The forms are then released and moved forward. At this point in the sequence, an entire span of segments is supported by an overhead gantry until it is post-tensioned and self-supporting. The truss or girder is then launched to the next adjacent pier, and the process is repeated. This type of construction usually requires additional clearances owing to the supporting truss. Even though the cross-sectional structural stiffness is high and the structural behavior after construction has been completed is comparatively simple, precautions must be taken during conveyance and construction because each sequence is complicated and the segments are very heavy [1]. Construction of precast segmental box girder bridges erected using the span-by-span method must consider the moment redistribution that takes place over the service life of the structure because of the time-dependent deformation of the concrete and the repeated changes in the structural system that occur during construction [2]. This means that to preserve the safety and serviceability of the bridge an analysis must be performed that considers the construction sequence. In particular, during assembly of the segments, each new segment that is positioned by the temporary overhead gantry or form traveler must be post-tensioned to the previous segment by using an external temporary tendon to maintain the continuity of the segments. At this point in the sequence, the stress in the bottom slab of the segment suddenly changes due to the post-tensioning, and there is a risk that the slab will either crack or collapse. Cracking of a bridge that spans seawater can lead to additional corrosion of the steel bars and prestressing of the tendons during its service life. Therefore, precise analysis of the structural system response of precast segment box girder bridges is required for each change in loading that occurs during the construction sequence [3]. This study addressed the structural system response of a precast segment box girder bridge. The stress state
in the temporary tensioning phase, when a prestressing steel bar is used to combine a fore segment with the subsequent segment, was assessed, and the cause of hairline cracks that developed during construction was examined. A countermeasure to control the cracking is proposed. The effect of design variables such as the sectional properties and tensioning procedures of the steel bars are considered in the countermeasure. Therefore, the proposed technique is practical and may be used to improve quality control and safety during the construction of precast segmental box girder bridges.
2. Crack patterns and cause of crack propagation 2.1. Construction sequence and NDT results The box girder bridge considered in this paper was designed and constructed using the span-by-span method and supported with an overhead gantry, as shown in Fig. 2. Numerous longitudinal hairline cracks were found on the bottom slabs of the box girder during the initial service life. A NDT test and FE analysis were performed on the box girder between Piers No. 5 and 6 in Fig. 1, and on the box girder between Piers No. 87 and 88, in Fig. 1. 2.1.1. Construction sequence and method Figs. 2 and 3 show the construction sequence of the box girder, and Fig. 3(b) depicts the position of the anchorages and the stressing sequence for temporary post-tensioning. The assembly procedure for the segments was: (1) spread epoxy on the joint of each segment, (2) apply temporary jacking to the attached segments, (3) install a wedge for spacing, and (4) cast the closure joint. The construction details are shown in Fig. 2. An analysis of the construction showed that a temporary prestressing compressive stress of more than
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Fig. 2. Falsework and assembling of segment.
3.4 MPa was applied to the segment joints. In addition, 600 kN of temporary prestressing was introduced over three steps, ! ! , from each of the five prestressing steel bars shown in Fig. 3(b). 2.1.2. Crack patterns and NDT results An inspection of a precast box girder bridge found numerous longitudinal cracks on the bottom slabs, as shown Fig. 4. The nondestructive test results, such as the Schmidt hammer test and PUNDIT test, are summarized in Table 1. Pundit test uses the through transmission method of ultrasonic pulse to determine material characteristics, such as compressive strength and depth of crack. It generates low-frequency ultrasonic pulses and measures the time taken for them to pass from one transducer to the other. It has become part of many national standards for concrete testing [4]. The ultrasonic equipment used in this study consisted of pulser/ receiver pundit device. The device generates and receives
ultrasonic waves and has a digital display of the results. The device can be used with piezoelectric transducers over a frequency range from 20 to 500 kHz. The pundit device was used to read the time required for ultrasonic waves to transfer across the specimen. The distance between the transducers, which is 30 cm, was divided by the measured time to calculate the wave velocity. Four readings were performed for each specimen and averaged. The crack depth was estimated from the PUNDIT test using the BS method [4], sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð4T 21 T 22 Þ h ¼ 150 ð1Þ ðT 22 T 21 Þ where h is the crack depth, and T1 and T2 are the ultrasonic delivery times at an estimated spacing of 15 and 30 cm along the crack. The average crack depth calculated from Eq. (1) was within 10 cm of the observed
D.-Y. Moon et al. / Computers and Structures 83 (2005) 2584–2593
Fig. 3. Construction sequence and cross-section of precast segment box girder bridge: (a) construction sequence (the numbers , mean the position of temporary tendons and the prestressing sequence) and (b) cross-section.
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and
Fig. 4. Crack details and overall crack patterns of bridge: (a) typical crack patterns and (b) crack patterns.
values. These are summarized in Table 2. The cracks propagated from the segment joints. The crack width ranged between 0.1 and 0.25 mm, and the crack length ranged between 50 and 100 cm. Additional extensions or further crack development did not occur. 2.1.3. Hypothetical cause of crack propagation The crack patterns and the possibility of existing cracks propagating further were evaluated with a visual
inspection of the inside and outside of the box girder bridge. Nondestructive ultrasonic and Schmidt hammer tests were used to estimate the concrete strength and crack depths. The inspection revealed that all cracks that developed on the bottom slab of the box girder propagated from a segment joint. We assumed that these cracks were not caused by manufacturing errors such as dry shrinkage and insufficient concrete cover because each segment box was cast, cured, and transported to
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Table 1 The compressive strength of concrete based on the NDT Estimated strength (MPa)
Bottom slab of box girder between P5 and P6 Bottom slab of box girder between P87 and P88
Schmidt hammer
St. dev.
PUNDIT
St. dev.
42.12 44.05
5.62 6.15
52.55 53.21
1.9 2.66
Table 2 The estimated crack depth
Bottom slab of box girder between P5 and P6 Bottom slab of box girder between P87 and P88
Average (cm)
St. dev.
8.2
0.85
8.4
0.93
the bridge site following precise quality control measures. Therefore, either the cracks developed owing to the self-weight of the segment box girder supported by the overhead gantry, or the cracks were propagated because the local tensile stress in the bottom slab was greater than the tensile strength of the concrete when temporary prestressing steel bars were stressed to bond the epoxy between the segments during the construction sequence.
Fig. 5. FE analysis model.
2.2. Finite element analysis for crack assessment Each of the two possible crack causes was evaluated through a finite element (FE) analysis. The commercial structural analysis program MIDAS [5], which was developed in Korea, was used. The concrete section and prestressing steel bars were modeled by eightnode solid element and as bar elements, respectively. 2.2.1. Risk estimate of crack propagation by excessive dead load The box segment depicted in Fig. 3(b) was modeled to estimate the risk of crack propagation caused by the dead load bending moment of the moving precast segment when it was positioned or moved in place by the overhead gantry. The material properties used in the analysis were the existing design data and NDT results. The compressive strength and elastic modulus of the concrete were 45 MPa and 2.93 · 104 MPa, respectively. The segment box was supported on the launching truss as depicted in Fig. 2, and roller conditions were assumed in the FE model as shown in Fig. 5. The stress contours of segment obtained from the FE analysis are depicted in Fig. 6. The maximum compressive stress and the maximum tensile stress in the top slab of the segment was 1.72 and 2.0 MPa, respectively. Because the mid-span tensile stress in the bottom slab,
Fig. 6. Stress contour and deformation by dead load.
where the cracks developed in the actual segment box was only 0.7 MPa, there was no possibility that the cracks developed as a result of the dead load during the moving or positioning phases. 2.2.2. Risk estimate of crack propagation as a result of external prestressing by the temporary tendon In this analysis, the two segments that were positioned on a truss after the epoxy bonding procedure were considered to be a perfectly bonded structure, as shown in Fig. 7, to evaluate the risk of crack propagation being caused by the external temporary prestressing steel bars. In this analysis, the temporary prestressing steel bars were modeled as truss elements with an elastic modulus of 2.0 · 105 MPa.
D.-Y. Moon et al. / Computers and Structures 83 (2005) 2584–2593
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Fig. 7. Modeling of prestressing sequence: (a) prestressing sequence and (b) after prestressing.
The supports for the two segments positioned on a falsework truss were modeled using the roller condition, and the end section of the previously launched segment nearest to the pier was modeled with hinges. The FE model for this analysis is depicted in Fig. 8. The temporary prestressing applied in the three steps ( ! ! ) shown in Fig. 3 was analyzed in the same manner. The deformation shapes obtained from the FE analysis for each segment after external prestressing are shown in Fig. 9. After temporary prestressing was applied to structurally integrate the two segments, upward and downward deformations occurred in the top and bottom slabs, respectively, of the two segments. The deformation of the second segment, which had a free end, was larger. In particular, an unexpectedly large local deformation occurred in the nearby anchor blocks that were placed on the bottom slab of the second segment to anchor the temporary tendons. This defor-
mation characteristic was very different from either the overall deformation of the segments during the construction sequence or the structural behavior of the entire bridge system caused by live loads once construction was completed. These deformation patterns and stress variations in the segments during construction could not be predicted from the results of the conventional construction sequence analysis based on a frame analysis. The deformation and stress contours of the bottom slab in the same direction are depicted in Fig. 10. The maximum tensile stress in the bottom slab of the second segment, which occurred in the actual crack propagation region, was 4.03 MPa. This stress is similar pffiffiffiffi to the rupture modulus of concrete (fr ¼ 0:63 fc0 ¼ 4:24 MPa, fc0 ¼ 45:0 MPa) [6]. Therefore, the risk of a crack occurring during the external prestressing state was greater then that during the other construction sequences.
Fig. 8. Support condition of FE model: (a) FE model, (b) side view and (c) plan view.
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Fig. 9. Deformation of the segment after temporary prestressing.
Fig. 10. Deformation and stress contour of segment 1 by temporary prestressing in original case: (a) stress contour of top slab, (b) stress contour of bottom slab, (c) deflection in front view and (d) half section.
3. Case studies of the prestressed concrete box design parameters The authors wished to investigate the structural behavior and stress variation of a segment during the temporary prestressing phase using a 3-dimensional FE analysis, and to propose an effective construction technique to control cracking during construction phases
using analytical results based on a parametric study. Differences in the structural behavior owing to design variables, such as the sequence of the temporary prestressing bars (Case 1), thickness of the bottom slab of the segment (Case 2), and the anchorage position of the prestressing bars (Case 3), were analyzed and related to the sectional deformation and stress distribution in the segment.
D.-Y. Moon et al. / Computers and Structures 83 (2005) 2584–2593
3.1. Effect of the temporary prestressing sequence (Case 1) The effect of the construction sequence that was followed as the temporary prestressing steel bars were jacked to form a web to the bottom slab of the segment was analyzed by reversing the prestressing steps (( ! ! in Fig. 3(b)). The resulting stresses and deformation are summarized in Table 3 and Fig. 10, and the final deformation after prestressing by the temporary steel bars is shown in Fig. 11. The tensile stress in the bottom slab was 0.4 MPa lower after the first and second prestressing states as compared to the stress obtained following the original sequence ( ! ! ). However, the final stresses after the temporary prestressing were almost the same. While the deformation of the bottom slab in the first and second prestressing phases was deliberately changed, the final deformation of the bottom slab after the third external prestressing phase was relatively large and almost equal to the deformation in the original case. For the top slab, however, an upward deformation occurred in the first prestressing stage, but the slab then recovered owing to the additional stressing, contrary to what was observed in the original design. 3.2. Effect of bottom slab thickness (Case 2) In this analysis, the thickness of the bottom slab was increased from 20 cm to 30 cm. From the results, the Table 3 Analytical stress at crack
Original design Case 1 Case 2 Case 3
Step 1 (MPa)
Step 2 (MPa)
Step 3 (MPa)
4.01 3.60 2.50 1.73
4.02 3.60 2.52 1.76
4.03 4.03 2.53 2.17
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tensile stress of the bottom slab was 2.5 MPa, or approximately 1.5 MPa less than the stress of the original segment. The deformation profile caused by the stressing sequence was similar to that observed with the original slab, but the deformation of the bottom slab decreased by 60%. This resulted from the stiffness increment of the bottom slab and verified that increasing the thickness of the bottom slab was an effective means of crack control. However, increasing the thickness also increased the dead load and reduced the structural efficiency of the segment. 3.3. Effect of the anchorage position (Case 3) An alternative segment box was analyzed, in which the anchor blocks that were used to attach the external temporary prestressing steel bars were moved to the joint of the web and the bottom slab, from the midpoint of the bottom slab, as depicted in Fig. 3(b). The deflection and stress contours of the alternative segment box model are shown in Fig. 12. From the results, the tensile stress of the bottom slab greatly decreased to 2.17 MPa. As depicted in Fig. 11, the deformation of the bottom slab in Case 3 decreased remarkably as compared to the other cases, while the deformation of the top slab was similar to the other cases. The change in deflection at each prestressing step was relatively small, within 0.1 mm. Therefore, moving the anchoring positions was the more effective technique for controlling cracking during construction. The theoretical deflection change depended on the prestressing steps, which followed the procedure described in the primary design plan shown in Fig. 13. In the figure, the y-axis gives the maximum deformation of the top and bottom slabs of the second segment (Segment in Fig. 9) at each prestressing step. The initial deformation of the segment caused by the dead load prior to prestressing was assumed to be 0, and is denoted as ÔReferenceÕ in the figure. Also, (+) is an upward deformation to the reference level of the top slab and () is a
Fig. 11. The comparison original deformation with other cases: (a) original case, (b) Case 1, (c) Case 2 and (d) Case 3.
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Fig. 12. FE model and results of Case 3: (a) modeling and (b) half section.
2
Original case
0.15
Case1
1.5
0.1
Case 2
1
0.05
Case 3
0 -0.05
Reference
Step 1
Step 2
Step 3
Deflection(mm)
Deflection(mm)
0.2
-0.1
0 Reference -0.5 -1
-0.15
a
0.5
-1.5 Prestressing sequence
b
Step 1 Original case Case1 Case 2 Case 3
Step 2
Step 3
Prestressing sequence
Fig. 13. The deflection variation of prestressing sequences: (a) top slab and (b) bottom slab.
downward deformation to the reference level of the bottom slab. The increment of the upward deformation in the bottom slab was higher after the first step, and the increment after additional prestressing at the web of the segment was relatively small. For the top slab, a downward deformation occurred owing to prestressing of the bottom slab, but the slab recovered smoothly from the additional jacking of the prestressing tendon in the upper web of the segment. The stresses acting in the transverse direction obtained from the FE analysis are summarized in Table 3. Excessive deformation and tensile stresses caused by either the prestressing force in the bottom slab or an insufficient bottom slab thickness can be assumed to be the cause of the longitudinal cracks that developed on the bottom surface of the lower slab of the segment. This takes into account the identical crack patterns and analytical results.
bottom slab of the segment box in a direction parallel to the bridge. These were caused by excessive tensile stresses and the deformation that occurred during temporary external prestressing for bonding the adjacent segment box. The thickness of the bottom slab and the anchoring position of the external prestressing bars were the dominant factors that affected the tensile stresses in the bottom slab of the segment. Consequently, a proposal to move the anchoring positions and thereby decrease the stress and deformation of the segment box during the external prestressing sequence was verified using a FE analysis. This was found to be a more effective technique than other proposals for preventing cracks during construction, when the efficiency of the section and construction costs were considered.
References 4. Conclusions The authors investigated the stress variation and deformation characteristics of a segment during the construction of an actual precast segment box girder bridge, using a sequence analysis, and verified proposed construction techniques to control the cracks that developed during construction. A FE analysis and NDT results showed that longitudinal cracks developed on the
[1] Menn C. Prestressed concrete bridges. Boston: Birkhauser; 1990. [2] Kwak HG, Seo Y-J. Time-dependent behavior of composite beams with flexible connectors. Comput Meth Appl Mech Eng 2002;191(34):3751–72. [3] Megally S, Seible F, Garg M, Dowell RK. Seismic performance of precast segmental bridge superstructures with internally bonded prestressing tendons. PCI J 2002;47: 40–56.
D.-Y. Moon et al. / Computers and Structures 83 (2005) 2584–2593 [4] BS 4408: pt.5. Non-destructive methods of test for concretemeasurement of the ultrasonic pulses velocity in concrete. British Standard Institution, London, UK, 1970.
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[5] MIDAS IT Co., MIDAS Manual, Seoul, Korea, 2001. [6] Concrete Design Specification, Korean Concrete Institute, Seoul, Korea, 2000.
Practical crack control during the construction of precast segmental box girder bridges Do-Young Moon a, Jongsung Sim a, Hongseob Oh a b
b,*
Department of Civil and Environmental Engineering, Hanyang University, 1271 Sa1-dong, Ansan 425-791, South Korea Department of Civil Engineering, Jinju National University, 150 Chilam-dong, Jinju, Kyeongnam 660-758, South Korea Received 7 October 2004; accepted 16 May 2005 Available online 12 September 2005
Abstract Cracks that occurred in the bottom slab of a precast segmental bridge were investigated through a construction sequence analysis, which revealed that the cracks were caused by excessive deformation during temporary post-tensioning while joining the segments. In addition, a parametric study was performed to evaluate the effects of the prestressing sequence, bottom slab thickness, and position of the prestressing anchors. The structural behavior of the girder sections was greatly affected by the thickness of the bottom slab and the position of prestressing anchors, but not by the prestressing sequence. Based on the results, a construction method that prevents the cracks is proposed. 2005 Elsevier Ltd. All rights reserved. Keywords: Construction sequence analysis; FE analysis; PC box girder; Precast segmental bridge; Structural behavior; Temporary prestressing
1. Introduction Prestressed concrete box girder bridges were developed in Europe in the 1950s, and are widely used in both mid- and long-span bridge construction for reasons of economy and aesthetics. In particular, quality control is easily ensured when precast segmental box girder bridges are constructed using the span-by-span method, because the mechanization of the construction work allows contracts for the spans to be awarded for a term that extends over many construction projects. Therefore, this technique has been used in many of the prestressed concrete girder bridges constructed in Korea since 1980. * Corresponding author. Tel.: +82 55 751 3299; fax: +82 55 751 3209. E-mail address: [email protected] (H. Oh).
The Seo-hae grand bridge, which is an oversea bridge with a total length of 7.3 km that was completed in early 2001, also used this method, except for the cable-stayed portion of the bridge, as shown in Fig. 1. In precast segmental construction, the bridge segments are constructed offsite. They are then trucked or barged to the bridge site and lifted into place with a crane or gantry, as depicted in Fig. 2. The size of the segments is affected primarily by the method of transport that is available. For example, a bridge located near a navigable waterway can use larger segments because they can be transported by barge. If the segments must be transported by truck, they are generally limited to widths that can travel within a roadway lane. In the span-by-span method, a segmental box is placed on the pier, moved by an overslung truss, and posttensioned after it has been erected.
0045-7949/$ - see front matter 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.compstruc.2005.05.001
D.-Y. Moon et al. / Computers and Structures 83 (2005) 2584–2593
2585
PSM FCM
Dangjin
PSM Cable stayed Bridge
P100 A2 P74
PSM P56 P55 FCM
Pier87~ Pier88
P41 P40
Pyungtak
Pier5~ Pier6
Fig. 1. The bridge plans and inspected bridge section.
The forms are then released and moved forward. At this point in the sequence, an entire span of segments is supported by an overhead gantry until it is post-tensioned and self-supporting. The truss or girder is then launched to the next adjacent pier, and the process is repeated. This type of construction usually requires additional clearances owing to the supporting truss. Even though the cross-sectional structural stiffness is high and the structural behavior after construction has been completed is comparatively simple, precautions must be taken during conveyance and construction because each sequence is complicated and the segments are very heavy [1]. Construction of precast segmental box girder bridges erected using the span-by-span method must consider the moment redistribution that takes place over the service life of the structure because of the time-dependent deformation of the concrete and the repeated changes in the structural system that occur during construction [2]. This means that to preserve the safety and serviceability of the bridge an analysis must be performed that considers the construction sequence. In particular, during assembly of the segments, each new segment that is positioned by the temporary overhead gantry or form traveler must be post-tensioned to the previous segment by using an external temporary tendon to maintain the continuity of the segments. At this point in the sequence, the stress in the bottom slab of the segment suddenly changes due to the post-tensioning, and there is a risk that the slab will either crack or collapse. Cracking of a bridge that spans seawater can lead to additional corrosion of the steel bars and prestressing of the tendons during its service life. Therefore, precise analysis of the structural system response of precast segment box girder bridges is required for each change in loading that occurs during the construction sequence [3]. This study addressed the structural system response of a precast segment box girder bridge. The stress state
in the temporary tensioning phase, when a prestressing steel bar is used to combine a fore segment with the subsequent segment, was assessed, and the cause of hairline cracks that developed during construction was examined. A countermeasure to control the cracking is proposed. The effect of design variables such as the sectional properties and tensioning procedures of the steel bars are considered in the countermeasure. Therefore, the proposed technique is practical and may be used to improve quality control and safety during the construction of precast segmental box girder bridges.
2. Crack patterns and cause of crack propagation 2.1. Construction sequence and NDT results The box girder bridge considered in this paper was designed and constructed using the span-by-span method and supported with an overhead gantry, as shown in Fig. 2. Numerous longitudinal hairline cracks were found on the bottom slabs of the box girder during the initial service life. A NDT test and FE analysis were performed on the box girder between Piers No. 5 and 6 in Fig. 1, and on the box girder between Piers No. 87 and 88, in Fig. 1. 2.1.1. Construction sequence and method Figs. 2 and 3 show the construction sequence of the box girder, and Fig. 3(b) depicts the position of the anchorages and the stressing sequence for temporary post-tensioning. The assembly procedure for the segments was: (1) spread epoxy on the joint of each segment, (2) apply temporary jacking to the attached segments, (3) install a wedge for spacing, and (4) cast the closure joint. The construction details are shown in Fig. 2. An analysis of the construction showed that a temporary prestressing compressive stress of more than
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D.-Y. Moon et al. / Computers and Structures 83 (2005) 2584–2593
Fig. 2. Falsework and assembling of segment.
3.4 MPa was applied to the segment joints. In addition, 600 kN of temporary prestressing was introduced over three steps, ! ! , from each of the five prestressing steel bars shown in Fig. 3(b). 2.1.2. Crack patterns and NDT results An inspection of a precast box girder bridge found numerous longitudinal cracks on the bottom slabs, as shown Fig. 4. The nondestructive test results, such as the Schmidt hammer test and PUNDIT test, are summarized in Table 1. Pundit test uses the through transmission method of ultrasonic pulse to determine material characteristics, such as compressive strength and depth of crack. It generates low-frequency ultrasonic pulses and measures the time taken for them to pass from one transducer to the other. It has become part of many national standards for concrete testing [4]. The ultrasonic equipment used in this study consisted of pulser/ receiver pundit device. The device generates and receives
ultrasonic waves and has a digital display of the results. The device can be used with piezoelectric transducers over a frequency range from 20 to 500 kHz. The pundit device was used to read the time required for ultrasonic waves to transfer across the specimen. The distance between the transducers, which is 30 cm, was divided by the measured time to calculate the wave velocity. Four readings were performed for each specimen and averaged. The crack depth was estimated from the PUNDIT test using the BS method [4], sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð4T 21 T 22 Þ h ¼ 150 ð1Þ ðT 22 T 21 Þ where h is the crack depth, and T1 and T2 are the ultrasonic delivery times at an estimated spacing of 15 and 30 cm along the crack. The average crack depth calculated from Eq. (1) was within 10 cm of the observed
D.-Y. Moon et al. / Computers and Structures 83 (2005) 2584–2593
Fig. 3. Construction sequence and cross-section of precast segment box girder bridge: (a) construction sequence (the numbers , mean the position of temporary tendons and the prestressing sequence) and (b) cross-section.
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and
Fig. 4. Crack details and overall crack patterns of bridge: (a) typical crack patterns and (b) crack patterns.
values. These are summarized in Table 2. The cracks propagated from the segment joints. The crack width ranged between 0.1 and 0.25 mm, and the crack length ranged between 50 and 100 cm. Additional extensions or further crack development did not occur. 2.1.3. Hypothetical cause of crack propagation The crack patterns and the possibility of existing cracks propagating further were evaluated with a visual
inspection of the inside and outside of the box girder bridge. Nondestructive ultrasonic and Schmidt hammer tests were used to estimate the concrete strength and crack depths. The inspection revealed that all cracks that developed on the bottom slab of the box girder propagated from a segment joint. We assumed that these cracks were not caused by manufacturing errors such as dry shrinkage and insufficient concrete cover because each segment box was cast, cured, and transported to
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Table 1 The compressive strength of concrete based on the NDT Estimated strength (MPa)
Bottom slab of box girder between P5 and P6 Bottom slab of box girder between P87 and P88
Schmidt hammer
St. dev.
PUNDIT
St. dev.
42.12 44.05
5.62 6.15
52.55 53.21
1.9 2.66
Table 2 The estimated crack depth
Bottom slab of box girder between P5 and P6 Bottom slab of box girder between P87 and P88
Average (cm)
St. dev.
8.2
0.85
8.4
0.93
the bridge site following precise quality control measures. Therefore, either the cracks developed owing to the self-weight of the segment box girder supported by the overhead gantry, or the cracks were propagated because the local tensile stress in the bottom slab was greater than the tensile strength of the concrete when temporary prestressing steel bars were stressed to bond the epoxy between the segments during the construction sequence.
Fig. 5. FE analysis model.
2.2. Finite element analysis for crack assessment Each of the two possible crack causes was evaluated through a finite element (FE) analysis. The commercial structural analysis program MIDAS [5], which was developed in Korea, was used. The concrete section and prestressing steel bars were modeled by eightnode solid element and as bar elements, respectively. 2.2.1. Risk estimate of crack propagation by excessive dead load The box segment depicted in Fig. 3(b) was modeled to estimate the risk of crack propagation caused by the dead load bending moment of the moving precast segment when it was positioned or moved in place by the overhead gantry. The material properties used in the analysis were the existing design data and NDT results. The compressive strength and elastic modulus of the concrete were 45 MPa and 2.93 · 104 MPa, respectively. The segment box was supported on the launching truss as depicted in Fig. 2, and roller conditions were assumed in the FE model as shown in Fig. 5. The stress contours of segment obtained from the FE analysis are depicted in Fig. 6. The maximum compressive stress and the maximum tensile stress in the top slab of the segment was 1.72 and 2.0 MPa, respectively. Because the mid-span tensile stress in the bottom slab,
Fig. 6. Stress contour and deformation by dead load.
where the cracks developed in the actual segment box was only 0.7 MPa, there was no possibility that the cracks developed as a result of the dead load during the moving or positioning phases. 2.2.2. Risk estimate of crack propagation as a result of external prestressing by the temporary tendon In this analysis, the two segments that were positioned on a truss after the epoxy bonding procedure were considered to be a perfectly bonded structure, as shown in Fig. 7, to evaluate the risk of crack propagation being caused by the external temporary prestressing steel bars. In this analysis, the temporary prestressing steel bars were modeled as truss elements with an elastic modulus of 2.0 · 105 MPa.
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Fig. 7. Modeling of prestressing sequence: (a) prestressing sequence and (b) after prestressing.
The supports for the two segments positioned on a falsework truss were modeled using the roller condition, and the end section of the previously launched segment nearest to the pier was modeled with hinges. The FE model for this analysis is depicted in Fig. 8. The temporary prestressing applied in the three steps ( ! ! ) shown in Fig. 3 was analyzed in the same manner. The deformation shapes obtained from the FE analysis for each segment after external prestressing are shown in Fig. 9. After temporary prestressing was applied to structurally integrate the two segments, upward and downward deformations occurred in the top and bottom slabs, respectively, of the two segments. The deformation of the second segment, which had a free end, was larger. In particular, an unexpectedly large local deformation occurred in the nearby anchor blocks that were placed on the bottom slab of the second segment to anchor the temporary tendons. This defor-
mation characteristic was very different from either the overall deformation of the segments during the construction sequence or the structural behavior of the entire bridge system caused by live loads once construction was completed. These deformation patterns and stress variations in the segments during construction could not be predicted from the results of the conventional construction sequence analysis based on a frame analysis. The deformation and stress contours of the bottom slab in the same direction are depicted in Fig. 10. The maximum tensile stress in the bottom slab of the second segment, which occurred in the actual crack propagation region, was 4.03 MPa. This stress is similar pffiffiffiffi to the rupture modulus of concrete (fr ¼ 0:63 fc0 ¼ 4:24 MPa, fc0 ¼ 45:0 MPa) [6]. Therefore, the risk of a crack occurring during the external prestressing state was greater then that during the other construction sequences.
Fig. 8. Support condition of FE model: (a) FE model, (b) side view and (c) plan view.
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Fig. 9. Deformation of the segment after temporary prestressing.
Fig. 10. Deformation and stress contour of segment 1 by temporary prestressing in original case: (a) stress contour of top slab, (b) stress contour of bottom slab, (c) deflection in front view and (d) half section.
3. Case studies of the prestressed concrete box design parameters The authors wished to investigate the structural behavior and stress variation of a segment during the temporary prestressing phase using a 3-dimensional FE analysis, and to propose an effective construction technique to control cracking during construction phases
using analytical results based on a parametric study. Differences in the structural behavior owing to design variables, such as the sequence of the temporary prestressing bars (Case 1), thickness of the bottom slab of the segment (Case 2), and the anchorage position of the prestressing bars (Case 3), were analyzed and related to the sectional deformation and stress distribution in the segment.
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3.1. Effect of the temporary prestressing sequence (Case 1) The effect of the construction sequence that was followed as the temporary prestressing steel bars were jacked to form a web to the bottom slab of the segment was analyzed by reversing the prestressing steps (( ! ! in Fig. 3(b)). The resulting stresses and deformation are summarized in Table 3 and Fig. 10, and the final deformation after prestressing by the temporary steel bars is shown in Fig. 11. The tensile stress in the bottom slab was 0.4 MPa lower after the first and second prestressing states as compared to the stress obtained following the original sequence ( ! ! ). However, the final stresses after the temporary prestressing were almost the same. While the deformation of the bottom slab in the first and second prestressing phases was deliberately changed, the final deformation of the bottom slab after the third external prestressing phase was relatively large and almost equal to the deformation in the original case. For the top slab, however, an upward deformation occurred in the first prestressing stage, but the slab then recovered owing to the additional stressing, contrary to what was observed in the original design. 3.2. Effect of bottom slab thickness (Case 2) In this analysis, the thickness of the bottom slab was increased from 20 cm to 30 cm. From the results, the Table 3 Analytical stress at crack
Original design Case 1 Case 2 Case 3
Step 1 (MPa)
Step 2 (MPa)
Step 3 (MPa)
4.01 3.60 2.50 1.73
4.02 3.60 2.52 1.76
4.03 4.03 2.53 2.17
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tensile stress of the bottom slab was 2.5 MPa, or approximately 1.5 MPa less than the stress of the original segment. The deformation profile caused by the stressing sequence was similar to that observed with the original slab, but the deformation of the bottom slab decreased by 60%. This resulted from the stiffness increment of the bottom slab and verified that increasing the thickness of the bottom slab was an effective means of crack control. However, increasing the thickness also increased the dead load and reduced the structural efficiency of the segment. 3.3. Effect of the anchorage position (Case 3) An alternative segment box was analyzed, in which the anchor blocks that were used to attach the external temporary prestressing steel bars were moved to the joint of the web and the bottom slab, from the midpoint of the bottom slab, as depicted in Fig. 3(b). The deflection and stress contours of the alternative segment box model are shown in Fig. 12. From the results, the tensile stress of the bottom slab greatly decreased to 2.17 MPa. As depicted in Fig. 11, the deformation of the bottom slab in Case 3 decreased remarkably as compared to the other cases, while the deformation of the top slab was similar to the other cases. The change in deflection at each prestressing step was relatively small, within 0.1 mm. Therefore, moving the anchoring positions was the more effective technique for controlling cracking during construction. The theoretical deflection change depended on the prestressing steps, which followed the procedure described in the primary design plan shown in Fig. 13. In the figure, the y-axis gives the maximum deformation of the top and bottom slabs of the second segment (Segment in Fig. 9) at each prestressing step. The initial deformation of the segment caused by the dead load prior to prestressing was assumed to be 0, and is denoted as ÔReferenceÕ in the figure. Also, (+) is an upward deformation to the reference level of the top slab and () is a
Fig. 11. The comparison original deformation with other cases: (a) original case, (b) Case 1, (c) Case 2 and (d) Case 3.
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Fig. 12. FE model and results of Case 3: (a) modeling and (b) half section.
2
Original case
0.15
Case1
1.5
0.1
Case 2
1
0.05
Case 3
0 -0.05
Reference
Step 1
Step 2
Step 3
Deflection(mm)
Deflection(mm)
0.2
-0.1
0 Reference -0.5 -1
-0.15
a
0.5
-1.5 Prestressing sequence
b
Step 1 Original case Case1 Case 2 Case 3
Step 2
Step 3
Prestressing sequence
Fig. 13. The deflection variation of prestressing sequences: (a) top slab and (b) bottom slab.
downward deformation to the reference level of the bottom slab. The increment of the upward deformation in the bottom slab was higher after the first step, and the increment after additional prestressing at the web of the segment was relatively small. For the top slab, a downward deformation occurred owing to prestressing of the bottom slab, but the slab recovered smoothly from the additional jacking of the prestressing tendon in the upper web of the segment. The stresses acting in the transverse direction obtained from the FE analysis are summarized in Table 3. Excessive deformation and tensile stresses caused by either the prestressing force in the bottom slab or an insufficient bottom slab thickness can be assumed to be the cause of the longitudinal cracks that developed on the bottom surface of the lower slab of the segment. This takes into account the identical crack patterns and analytical results.
bottom slab of the segment box in a direction parallel to the bridge. These were caused by excessive tensile stresses and the deformation that occurred during temporary external prestressing for bonding the adjacent segment box. The thickness of the bottom slab and the anchoring position of the external prestressing bars were the dominant factors that affected the tensile stresses in the bottom slab of the segment. Consequently, a proposal to move the anchoring positions and thereby decrease the stress and deformation of the segment box during the external prestressing sequence was verified using a FE analysis. This was found to be a more effective technique than other proposals for preventing cracks during construction, when the efficiency of the section and construction costs were considered.
References 4. Conclusions The authors investigated the stress variation and deformation characteristics of a segment during the construction of an actual precast segment box girder bridge, using a sequence analysis, and verified proposed construction techniques to control the cracks that developed during construction. A FE analysis and NDT results showed that longitudinal cracks developed on the
[1] Menn C. Prestressed concrete bridges. Boston: Birkhauser; 1990. [2] Kwak HG, Seo Y-J. Time-dependent behavior of composite beams with flexible connectors. Comput Meth Appl Mech Eng 2002;191(34):3751–72. [3] Megally S, Seible F, Garg M, Dowell RK. Seismic performance of precast segmental bridge superstructures with internally bonded prestressing tendons. PCI J 2002;47: 40–56.
D.-Y. Moon et al. / Computers and Structures 83 (2005) 2584–2593 [4] BS 4408: pt.5. Non-destructive methods of test for concretemeasurement of the ultrasonic pulses velocity in concrete. British Standard Institution, London, UK, 1970.
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[5] MIDAS IT Co., MIDAS Manual, Seoul, Korea, 2001. [6] Concrete Design Specification, Korean Concrete Institute, Seoul, Korea, 2000.